Chapter 4.4, Problem 45ES

If $f$ is a periodic function, then the locations of all absolute extrema on the interval $\left(-\infty ,+\infty \right)$ can be obtained by finding the locations of the absolute extrema for one period and using the periodicity to locate the rest. Use this idea in these exercises to find the absolute maximum and minimum values of the function, and state the x-values at which they occur.

$f\left(x\right)=2\cos x+\cos 2x$